Let the function, $$f(x)=\begin{cases}-3ax^{2}-2, & x < 1\\a^{2}+bx, & x \geq 0\end{cases}$$ be differentiable for all  $$x \in R,  $$ where $$ a>1, b \in R$$.  If the area of the region enclosed by $$ y=f(x) \text{and the line } y= -20 \text{ is } \alpha+\beta\sqrt{3},\alpha, \beta \in Z$$,  then the value of  $$\alpha + \beta \text{ is } $$_______